The draw means Everton retain their eight-point lead over Boro in the battle for a Champions League place at the end of the season.
The game was played at a cracking pace and in a competitive spirit, with Everton hitting back to equalise in the second half.
Middlesbrough welcomed Ugo Ehiogu back to league action but Everton were without Leon Osman.
Former Southampton striker James Beattie made his second appearance for Everton following his £6million transfer to Goodison earlier this month.
However, Boro suffered an early blow when Ehiogu limped out of the action in the 15th minute.
It looked as though the former Aston Villa player had aggravated a knee injury and there was sympathetic applause from the crowd as he trudged towards the dressing room.
Ehiogu has endured an injury-ravaged season and it looks as though the towering central defender could face a lengthy lay-off.
Veteran defender Colin Cooper, who earlier this month made his 600th career appearance, took over from Ehiogu alongside skipper Gareth Southgate.
Everton were unlucky not to take the lead when Lee Carsley struck the crossbar with a shot following a left-wing Kevin Kilbane cross.
Carsley looked marginally offside but no flag was raised and the player could consider himself unlucky with an effort that beat Mark Schwarzer.
However, Boro went ahead in the 25th minute when Boudewijn Zenden burst through on the left to accept a Jimmy Floyd Hasselbaink pass.
The Dutch international moved into the penalty area and then chipped the ball over Richard Wright, with Everton skipper Alan Stubbs making a desperate but forlorn attempt to clear the effort off the line.
Boro soon had the ball in the net again but the cries of their fans quickly died when they realised that the referee had blown for a foul.
The game was being played at a frantic pace and neither defence had a chance to settle. Hasselbaink fired just wide in a bid to end his goal drought as Boro continued to show more threat despite the quick counter-attacks of the visitors.
However, only a brilliant Schwarzer save denied Marcus Bent an equaliser just before the break.
Early in the second half Schwarzer collected a Stubbs header when the Everton skipper should have done better while Beattie was booked for a foul when he raced back to help out his defence.
Wright saved Zenden's shot at the near post before Middlesbrough withdrew Slovakian striker Szilard Nemeth and sent on youngster James Morrison.
Schwarzer was having a nervy game and was fortunate when Beattie shot against an upright after the goalkeeper had failed to collect the ball. With no-one on the goal-line it was a relief for Boro when the ball hit a post.
Beattie has an impressive scoring record at the Riverside Stadium and he must have felt he had enhanced that as he lay on the ground.
Everton sent on striker Duncan Ferguson and the veteran striker made an immediate impact as, from his header, Tim Cahill scored from close range.
Shortly after the equaliser, Schwarzer lay injured after Ferguson's late challenge, and the incident sparked a melee involving at least a dozen players. The referee took no action - it was difficult to single out one player - but then issued a "cool it" warning to the two skippers.
Bent missed a great Everton chance in the final minute but a goal at this stage would have been an injustice to the home side.